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The origin of cyclic period changes in close binaries: the case of

the Algol binary WW Cygni

Robert T. Zavala1,2, Bernard J. McNamara3 , Thomas E. Harrison4, Eduardo Galvan, Javier

Galvan, Thomas Jarvis, GeeAnn Killgore, Omar R. Mireles, Diana Olivares, Brian A. Rodriguez,

Matthew Sanchez, Allison L. Silva, Andrea L. Silva, Elena Silva-Velarde

Department of Astronomy, New Mexico State University, Dept 4500 P. O. Box 30001, Las

Cruces, NM 88011

ABSTRACT

Years to decade-long cyclic orbital period changes have been observed in several

classes of close binary systems including Algols, W Ursae Majoris and RS Canum Ve-

naticorum systems, and the cataclysmic variables. The origin of these changes is un-

known, but mass loss, apsidal motion, magnetic activity, and the presence of a third

body have all been proposed. In this paper we use new CCD observations and the

century-long historical record of the times of primary eclipse for WW Cygni to explore

the cause of these period changes. WW Cygni is an Algol binary whose orbital period

undergoes a 56 year cyclic variation with an amplitude of ≈ 0.02 days. We consider and

reject the hypotheses of mass transfer, mass loss, apsidal motion and the gravitational

influence of an unseen companion as the cause for these changes. A model proposed by

Applegate, which invokes changes in the gravitational quadrupole moment of the con-

vective and rotating secondary star, is the most likely explanation of this star’s orbital

period changes. This finding is based on an examination of WW Cygni’s residual O−C

curve and an analysis of the period changes seen in 66 other Algols. Variations in the

gravitational quadrupole moment are also considered to be the most likely explanation

for the cyclic period changes observed in several different types of binary systems.

Subject headings: binaries: eclipsing – stars: individual(WW Cygni) – stars: late type

– stars: rotation

1rzavala@nrao.edu

2Present address: National Radio Astronomy Observatory, P.O. Box 0, Socorro, NM 87801

3bmcnamar@nmsu.edu

4tharriso@nmsu.edu

– 2 –

1. Introduction

Long term cyclic period changes are a fairly common phenomenon in close binary systems.

These changes have been observed in Algols, RS Canum Venaticorum and W Ursae Majoris bi-

naries, and they are suspected to be present in Cataclysmic Variables (CVs)( Hall 1989; Hall &

Kreiner 1980; Hobart et al. 1994; Warner 1988). Researchers have found it difficult to quantify

this phenomenon because precise measurements extending over decades are required. The tradi-

tional manner in which period changes are investigated is through the construction of a plot of the

difference between a binary’s Observed and Calculated times of primary eclipse versus time. This

plot is referred to as an O−C diagram. Lanza & Rodono (1999) estimate that the median mod-

ulation period seen in these diagrams is 40-50 years for Algol and RS CVn systems while for CVs

this value varies from years to decades. The amplitudes of these waveforms are also small having

∆P/P = 10−7 − 10−6 for CVs, ∆P/P = 10−6 for W UMa binaries, and ∆P/P = 10−5 Algols and

RS CVns. Although the physical cause for these variations is not known, the similar appearance of

the O−C diagrams for several classes of close binaries suggests that a common mechanism produces

them.

Several hypotheses have been advanced to explain the cyclic period changes in close binaries.

Apsidal motion, which involves a change in the orientation of the binary’s major axis, is an un-

likely mechanism because close binaries possess circular orbits and this phenomenon only occurs

in systems having large eccentricities. If apsidal motion were present, the times for secondary and

primary minima would be shifted in opposite directions, but this effect is rarely seen and does not

appear to be present in Algols. An alternate possibility is that the cyclic pattern in the O−C plot

is caused by the presence of a third body. This idea has been explored by several investigators,

most recently by Borkovits & Hegedus (1996). These researchers postulate that the motion of the

binary around the center of mass of a triple system causes the primary and secondary eclipse times

to vary in a uniform and periodic fashion. In this case, the cyclic O−C pattern arises from orbital

induced changes in the distance to the observer. Finally, Hall (1989) noted that, for Algols which

possess alternating period increases and decreases, the spectral types of the secondaries are always

in the range late F to K. These stars have outer convective zones and, if they are rapidly rotating,

a magnetic dynamo is produced (Parker 1979). Applegate (1992) and Lanza, Rodono, and Rosner

(1998) used this information to develop a theory to explain the cyclic shape of the O−C curves

of these systems. They suggest that if the secondary is deformed by tidal and centrifugal forces,

changes in the internal rotation associated with a magnetic activity cycle alter the star’s gravita-

tional quadrupole moment. As the quadrupole moment increases the gravitational field increases,

leading to a decrease in the binary period. Conversely, when the quadrupole moment decreases,

the binary period increases (Lanza & Rodono 1999).

In this paper we will use an extraordinarily long O−C curve for WW Cygni to examine whether

the above models can explain the cyclic pattern of period variations observed in this object. In

§2 we present our new observations of WW Cyg. In §3 an updated ephemeris is computed and

residuals in the O−C plot are discussed and in §4 the three models above are tested. Conclusions

– 3 –

are presented in §5.

2. Program Object and Observations

WW Cygni (HD 227457, BD+41 3595, HIP 98814) is a relatively bright Algol binary with

deep (∆v = 3.5mag) primary eclipses. WW Cyg’s visual magnitude varies from 10.0 to 13.5 with

a period of 3.3 days. This system’s brightness and large amplitude have made it a frequent source

of study with over a century of observations present in the literature (see Hall & Wawrukiewicz

1972 and references therein). Struve (1946) established the spectral type of the primary (mass-

gaining) star as B8 and speculated that the secondary (mass-losing) star was type G. Yoon et

al. (1994) subsequently assigned the secondary a spectral class of G9, but due to a paucity of

sub-giant calibration stars they were unable to determine its luminosity class. They also noted

that photometrically determined spectral types for Algol secondaries are typically later than those

determined spectroscopically.

Multicolor CCD observations of WW Cyg were acquired at the Clyde Tombaugh Campus

Observatory on the campus of New Mexico State University between October 1997 and October

1999. The observatory is equipped with a 16 inch F/10 Meade LX 200 Schmidt-Cassegrain telescope

and a Santa Barbara Instruments Group ST8 CCD camera. The camera uses a KAF1600 CCD

with 1520×1020 9µm pixels. Readnoise and gain were experimentally determined to be 11 e−pix−1

and 2.5 e−ADU−1 (Massey & Jacoby 1992). The camera is equipped with UBVRI filters which

match the prescription of Bessell (1990). Due to the system’s poor sensitivity in U, no observations

were collected in this filter. Because the chip plate scale is 0.46 arc seconds/pixel and typical

seeing at the observatory is 2.5-3”, pixels were binned by two prior to readout. This procedure

decreased the normal readout time from one minute to 15 seconds. Images were stored on a laptop

computer whose internal clock was set at the beginning of each night using a UTC time signal

from a GOES weather satellite. Occasional checks of the accuracy of the clock were made during

an observing run by initiating exposures synchronously with the WWVB time signal received via

shortwave. Exposures were 120 seconds in B, 60 seconds in V, and 30 seconds in R and I. On

two occasions (UT 1998 September 01 and October 11) observations were acquired in V only to

reduce the sampling time interval so that a more precise determination of the time of primary

minimum could be obtained. Otherwise, with a few exceptions, the four filters were cycled in

the order BVRI. Data were reduced using the aperture photometry packages found in IRAF5 and

standard differential photometry techniques. The B solution was poor and therefore was not used.

Magnitudes for WW Cyg were obtained relative to two comparison stars from the HST Guide Star

Catalog: GSC 3158-1468 (V=12.08 and V−I=0.66) and 3158-1228 (V=11.51 and V−I=1.74). The

complete multi-color data will be presented in a later paper.

5IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of

Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.

– 4 –

3. Ephemeris and the O−C Curve

By definition, Algol systems involve mass transfer and therefore period changes are expected to

occur (Kwee & van Woerden 1958). To investigate these changes a new ephemeris was calculated

for WW Cyg and its century-long O−C curve was reexamined. Observations near primary eclipse

were obtained at NMSU on UT 1998 August 22, September 01, and October 11. The light curves

for these eclipses are shown in Figure 1, along with the comparison star data. Preliminary times of

minima (TOM) were then determined from a visual inspection of these observations. These times

were then refined using the algorithm of Kwee & van Woerden (1956) and a computer code kindly

provided by Dr. R. Nelson (2000, private communication) (see also Mallama 1982). The new TOM

are listed in Table 1 along with an earlier TOM determined by Buckner et al. (1998). A weighted

linear least squares fit to these TOM gives the following ephemeris

HJD = 2, 450, 387.6071 ± 0.0005 + (3.317813 ± 0.000003)E. (1)

Hall & Wawrukiewicz (1972) conducted a thorough literature search and produced an O−C

plot of WW Cyg through 1972 using the ephemeris of Graff (1922)

HJD = 2, 416, 981.3134 + 3.317676E. (2)

In Table 2 we list post 1972 O−C data with respect to Graff’s ephemeris. This allows us to extend

the O−C plot by almost 30 years. We plot the entire 107 year O−C data in Figure 2 together with

the best fit parabola,

C = 0.012 − 7.78 × 10−6E + 6.92 × 10−9E2, (3)

with all points weighted equally.

4. Discussion of the WW Cyg O−C Curve

The long term trend in Figure 2 indicates an increasing period. Assuming this trend is the

result of mass transfer we attempted an estimate of the mass transfer rate M . Kwee & van Woerden

(1958) derived a relationship for the change in the orbital period assuming total orbital angular

momentum is conserved while mass is transferred from one star to another. Reproducing equation

5 of Kwee & van Woerden (1958):

∆P/P = 3(ms/mp − 1)dms/ms, (4)

where ∆P is the change in the period P , ms is the mass of the secondary, mp is the mass of the

primary, and dms is the change in mass of ms. An estimate for the mass transfer rate in WW Cyg

– 5 –

can now be made. Between the ephemeris of Graff (1922) and equation 1 the period increased by

0.0002 days. Using the solution for WW Cyg presented by Hall & Wawrukiewicz (1972) the mass

of the secondary can be set to 2M⊙ and the mass ratio to ≈ 0.4. Over an elapsed time of 100 years

equation 4 gives as a mass transfer estimate

M = 7 × 10−7M⊙yr−1. (5)

This simplistic treatment of mass transfer is probably an underestimate of the actual mass transfer

rate. A more realistic model for non-conservative mass transfer is the wind-driven mass-transfer

model derived by Tout & Hall (1991). The mass transfer rate determined for the Algol U Cep in

Tout & Hall (1991) is an order of magnitude larger than the estimate above.

A careful examination of the O−C curve in Figure 2 shows that WW Cyg possesses an alter-

nating sequence of period increases and decreases superimposed upon a parabola. This behavior

is more easily seen in Figure 3 where the residuals from the parabolic fit are shown. Below we

examine three of the most widely discussed hypotheses used to explain this type of cyclic behavior.

a) Mass exchange or mass loss due to stellar winds: The most frequently mentioned explanation

for period changes in close binary systems is the transfer of mass from one star to another. However,

mass transfer from a less massive to a more massive component results in a steadily increasing period

not an alternating sequence of period increases and decreases. Mass transfer also appears to be an

unsuitable explanation for the cyclic O−C pattern seen in close binaries for another reason. The

RS CVn systems, in which cyclic O−C patterns are present, are in general detached systems (Hall

1976), so mass transfer cannot be invoked. Mass loss due to stellar winds also appears to be ruled

out. DeCampli and Baliunas (1979) have shown that for RS CVn stars the mass loss rates required

to produce a quasi-periodic signal in the O−C diagram are orders of magnitude larger than allowed

by observations. They note that such losses would conflict with the detection of soft x-rays from

α Aur, UX Ari, HR 1099, and RS CVn. If we assume a single process produces the cyclic O−C

curves, neither of these processes appear to be viable.

b) The Presence of a Third Body: The possibility that the cyclic O−C changes in Algols and

other short period binaries are due to the presence of a third star has been discussed by Frieboes-

Conde & Herczeg (1973), Chambliss (1992), and recently by Borkovits & Hegedus (1996). In

this model the binary revolves around the center of mass of the system thereby creating a regular

change in the observed period due to a light travel time effect (LTTE). Borkovits and Hegedus

tested this suggestion by incorporating the gravitational effects of a third body into fits of the

residual O−C curves of 18 close binaries. This model was able to produce qualitative agreement

between the observed and computed O−C curves for 4 systems (1 Algol, 3 W UMa) by solving for

the orbital elements of the assumed third body. In general, the mass of the third star was less than

0.5 M⊙ (with one exception) and therefore could have escaped detection. Marginal evidence for

a third body was presented for four other systems (all Algols). Marginal solutions required more

than one unseen companion and the mass for these companions, more than 2 M⊙ depending on

– 6 –

eccentricity, begins to present non-detection problems. For eight other systems LTTE solutions of

dubious reliability were obtained by Borkovits and Hegedus for the sake of completeness. LTTE

solutions could not be found for only two of the 18 binaries they studied. Motivated by this study

we used the O−C data for WW Cyg shown in Figure 2 to further test this hypothesis.

Kopal (1978) has shown that a third object orbiting a close binary creates a periodic pattern

in an O−C curve and that by describing this signal as a Fourier series, the orbital parameters of

the third body can be determined. Following the method adopted by Borkovits & Hegedus (1996),

we first subtracted the best-fit parabola shown in Figure 2 from the WW Cyg data. The power

spectra of these residuals were then computed and yielded a waveform having the parameters

R = 0.0187cos[2π(1.61 × 10−4)E − 1.2712], (6)

where R is the waveform of the residuals in days, E is the epoch, 1.61 ×10−4 is the inverse period

in epochs of Graff’s ephemeris, and the phase is −1.27 radians. This power spectrum is shown

in Figure 4 as a solid line. When equation 4 is plotted on the actual data (Figure 5a), it did not

provide a satisfactory fit. Consider the residuals in two groups; one from 1890 to 1940 and the other

from 1940 to 1998. The earlier group appears to have a narrow inverted V shape, and a shorter

period compared to the later group. Additionally, the observations of 1890-1900 and 1960-1972

deviate from the predicted form.

If the third body possesses an orbit with a nonzero eccentricity, the waveform contains both

fundamental and first harmonic terms. Adopting equation 6 as the fundamental, we searched for

its first harmonic at twice the frequency of the fundamental. The fundamental was subtracted from

the data and the power spectrum was recomputed, but the subsequent power spectrum was found

to be noise dominated (see lower dashed curve in Figure 4). We then used an iterative non-linear

least squares fitting routine, based on the Marquardt algorithm (Press et al. 1992) to determine

the parameters of the first harmonic. This program seeks to identify individual coefficients by

varying designated input values so that the sum of the squares of the residuals are minimized. As

an initial guess, an amplitude of 10 percent of the fundamental was employed since this value was

similar to that found by Borkovits & Hegedus (1996) for other close binaries. The parameters

of the fundamental (amplitude, frequency and phase) were fixed as was the frequency of the first

harmonic. According to Kopal (1978), the eccentricity of the third companion is given as

e = 2

√

a22 + b2

2

a21 + b2

1

(7)

where e is the eccentricity of the orbit and the ai’s and bi’s are the coefficients of the cosine and

sine terms respectively of the Fourier components of the O−C residuals. Our assumed amplitude

yields an eccentricity of ∼ 0.1. With the amplitude and phase of the first harmonic as the only

free parameters, the fitting routine consistently produced unrealistic eccentricities that were greater

– 7 –

than one. Fixing only the frequencies and leaving the amplitudes and phases of the two waveforms

as free parameters produced unrealistic fits to the data. Constraining the amplitude of the first

harmonic at 0.002 days and leaving the phase of the first harmonic as the only free parameter

resulted in an unacceptably high reduced χ2 of greater than 130. Based on these experiments, we

conclude that the third body hypothesis fails to explain the observed O−C curve for WW Cyg.

This agrees with the naive expectation from Figure 5a as the residuals do not appear to be strictly

periodic.

c) Magnetic cycles: In an important study comparing RS CVn to Algol binaries, Hall (1989)

found a striking correlation between the development of surface convection in the low mass sec-

ondary and the presence of an alternating orbital period. Hall’s plot, reproduced here as Figure

6, illustrates that when the secondary has a spectral type earlier than about F5 the orbital pe-

riod never displays an alternating pattern of period increases and decreases. For systems where

the secondary has a spectral type later that an F5, a significant number of binaries possess al-

ternating periods. Hall interpreted this finding as evidence that the onset of convection plays an

important role in producing cyclic period changes. Warner (1988) and Applegate & Patterson

(1987) attempted to explain the O−C patterns by assuming deformations of the star away from

hydrostatic equilibrium due to tidal or magnetic pressure effects, respectively. However, Marsh &

Pringle (1990) showed that tidal or magnetic pressure induced distortions in the active star away

from hydrostatic equilibrium were ruled out based on energetic considerations. Such distortions

could not be the method by which the quadrupole moment is deformed.

Applegate (1992) and Lanza, Rodono, and Rosner (1998) subsequently proposed that a

cyclic O−C pattern could be produced if the active star’s internal angular momentum distribution

changes as the star goes through a magnetic activity cycle similar to that of the Sun. Applegate

(1992) avoids the energy quandary mentioned above by maintaining fluid hydrostatic equilibrium

throughout the cycle. This was suggested as a common mechanism to explain the same alternating

period changes seen in W UMas, RS CVns, and CVs. This suggestion is consistent with the

observational evidence for RS CVn-like magnetic activity signatures in Algols (Richards 1990;

Richards & Albright 1993).

In the models of Applegate (1992) and Lanza, Rodono, and Rosner (1998), the rotational

oblateness of the late type star produces a change in the gravitational quadrupole moment, and

hence the orbit. In both models, the gravitational field of the primary is treated as originating

from a point mass. The field of the secondary is computed as arising from a point source located at

the star’s barycenter and a quadrupole moment term caused by tidal and rotational deformations.

Changes in the star’s effective angular velocity are then directly related to changes in the quadrupole

moment and to changes in the orbital period ( |∆Ω/Ω| ∼ |∆Q| ∼ |∆P/P|). The angular velocity

changes as a result of a torque supplied by the magnetic field in the outer convective region of the

late-type star. The presence of the required dynamo in the convective secondary stars is consistent

with the results of Lanza & Rodono (1999). Their analysis showed that the modulation period

of 46 close binaries supported the view that a dynamo operated in the outer atmospheres of the

– 8 –

secondary stars. The principal advantages of this model are that it presents a physically plausible

explanation whose time scale is in rough agreement with that seen in the O−C plots and that it

removes the need for strict periodicity.

Figure 6 demonstrates that there is no correlation of orbital period changes with mass ratio.

However, if the gravitational quadrupole moment term plays a dominant role in the creation of

cyclic period changes, a correlation may also exist between the occurrence of an alternating period

change and a binary’s orbital separation. Cyclic O−C variations should be more pronounced in

systems where the secondary star is most deformed, i.e. when the orbital separations are small.

Conversely, when the separations are large, the secondary star should not be as deformed and

cyclic variations should not be as pronounced. To test this idea we constructed Figure 7 which

shows whether these predictions are supported by the available data. As Hall did in Figure 6 we

selected Algols with convective secondaries from Giuricin, Mardirossian, & Mezzetti (1983). We

then searched the literature for published O−C curves for these systems and present the data in

Table 3. The columns in this table refer to the systems we selected, the secondary spectral type,

the binary period in days, nature of the period change, and the reference(s) for the O−C data.

In a few cases the secondary spectral type in Table 3 differs from that in Giuricin, Mardirossian,

& Mezzetti (1983). The reference for the updated secondary spectral type is given as a footnote

for these systems. The form of the period change noted in Table 3 follows the convention used

in Figure 6 with the same symbols being employed in Figure 7 for consistency. It is clear from

Figure 7 that alternating period variations are prominent in binaries with a period under 6 days and

that alternating period variations are less common in systems with larger orbital separations. We

consider this result to be suggestive, however more data is needed to confirm it. This is particularly

true for those systems not marked by an “X” which possess short periods. We note that the low

number of Algols with periods greater than 10 days is also insufficient to make a firm statement

about the nature of the O−C plots in this region of the diagram. Observational selection effects

probably play a role here because eclipse timings for these systems are more difficult to obtain.

Additionally, Giuricin, Mardirossian, & Mezzetti (1983) show that almost 80 percent of their 101

Algols have periods under 6.5 days.

Additional predictions of the Applegate model are that the brightness of the active star should

vary with the same period as seen in the O−C plot and that this change should be about 0.1

magnitude. Based on arguments about the manner in which kinetic and magnetic energy are

exchanged, Lanza & Rodono (1999) suggested that 0.1 magnitude is probably an upper limit.

Because the brightness change is caused by variations in the star’s differential rotation and not to

changes in its radius, the star should also be bluer when at maximum brightness.

These predictions were tested by Hall (1991) using the RS CVn system CG Cyg. The active

star in this system has a spectral type of G9.5V. Hall found that this system’s O−C curve possessed

a cyclic pattern with a period of about 52 years (see Figure 1 in Hall 1991). Using plots of this

object’s mean brightness and color while outside eclipse, he found that these quantities varied

with the same period as the O−C curve. He also found that this system was bluest when it was

– 9 –

brightest. Although Hall argued that these results confirmed the Applegate model, the magnitude

and color data he presented covered only about half of the 52 year cycle. This conclusion must

therefore be considered as tentative. Nevertheless, if Hall’s result is accepted, it suggests that, like

the Sun, the surface layer of the active star is spinning faster than its lower layers. We can perform

a similar, but cruder, analysis for WW Cyg. When Hall & Wawrukiewicz (1972) observed this star

on JD = 2440407.7 (Epoch 7061) it had a primary minimum of V=13.26 and dereddened colors

appropriate to a G2III or K0V. When we observed WW Cyg on JD= 2451057.8 (Epoch 10,268) it

had V=13.46 and dereddened V−R appropriate to a K2V. Examining Figure 5a, we found that the

times when the secondary was at its brightest(bluest) and faintest(reddest) were when the O−C

wave was at its maximum and minimum values, respectively. According to Applegate’s (1992)

model this implies that the surface layer of the secondary of WW Cyg is rotating more slowly

than its subsurface layer. This result differs with that found by Hall for the G9.5V star in CG

Cyg, which has a similar spectral type. This difference in rotational structure might appear to be

troubling but the secondary in WW Cyg is most likely a subgiant so this example does not provide

a direct comparison. Nevertheless, it does illustrate how long term period changes due to magnetic

activity may provide a probe of the interior structures of late-type stars in close binary systems.

5. Conclusions

WW Cyg, like several other close binaries, displays an alternating pattern in its times for

primary eclipse. We have explored three possible causes for this cyclic behavior: mass exchange

and mass loss due to stellar winds, the presence of a third body, and magnetic cycles. The first

two possibilities appear to be ruled out. However, the current evidence is consistent with the idea

that magnetic cycles within a lower mass secondary of spectral type later than F5, play a role.

Convection and rotation leading to magnetic dynamo activity have been theoretically shown to

produce cyclic changes in the gravitational field of the system. These changes are of sufficient

strength to produce orbital period changes of the observed size in close binaries. Additionally, the

time frame for these period changes is of the same order of magnitude as the magnetic cycles of

late type stars (Baliunas et al. 1995). Although we feel that the evidence at this point is not

conclusive, variations in the gravitational quadrupole moment caused by magnetic activity appears

to provide the best explanation for the cyclic behavior of the O−C curves observed in WW Cyg

and other close binary systems. More data are needed to construct a larger sample of O−C curves

for close binaries. We urge that both magnitude and color information be collected for a variety of

close binaries to show how the internal rotation of the late-type star changes with time. Because

several of these systems are relatively bright, this type of observational program is well suited to

facilities equipped with telescopes of modest aperture.

We are indebted to the many observers, amateur and professional, who amassed the wealth

of data on the eclipsing binaries listed in Table 3. This research has made use of the SIMBAD

– 10 –

database, operated at CDS, Strasbourg, France. This research has made use of NASA’s Astro-

physics Data System Abstract Service. NSF Grant HRD-9628730 supported this research. RTZ

gratefully acknowledges support from the New Mexico Alliance for Graduate Education and the

Professiorate through NSF Grant HRD-0086701.

REFERENCES

Applegate, J.H. 1992, ApJ, 385, 621

Applegate, J.H.,& Patterson, J. 1987, ApJ, 322, L99

Baldwin, M. E. & Samolyk, G. 1995, Observed Minima Timings of Eclipsing Binaries, Number 2

(Cambridge:AAVSO)

Baldwin, M. E. & Samolyk, G. 1996, Observed Minima Timings of Eclipsing Binaries, Number 3

(Cambridge:AAVSO)

Baldwin, M. E. & Samolyk, G. 1997, Observed Minima Timings of Eclipsing Binaries, Number 4

(Cambridge:AAVSO)

Baliunas, et al. 1995, ApJ, 438, 269

Batten, A. H. & Fletcher, J. M. 1978, PASP, 90, 312

Bessell, M. S. 1990, PASP, 102, 1181

Borkovits, T. & Hegedus, T. 1996, A&AS, 120, 63

Buckner, M., Nellermoe, B., & Mutel, R. 1998, IBVS, 4559

Chambliss, C.R. 1992 PASP, 104, 663

DeCampli, W. M. & Baliunas, S. L. 1979, ApJ, 230, 815

Degirmenci, O. L., Gulmen, O, Sezer, C., Erdem, A., & Devlen, A. 2000, A&A, 363, 244

Demircan, O., Akalin, A., Selam, S., & Mueyesseroglu, Z. 1995, A&AS, 114, 167

Derman, E. & Demircan, O. 1992, Ap&SS, 189, 309

Ertan, A. Y. 1981, ApSS, 77, 391

Etzel, P. B. & Olson, E. C. 1995, AJ, 110, 1809

Frieboes-Conde, H. & Herczeg, T. 1973, A&AS, 12, 1

Giuricin, G. & Mardirossian, F. 1981, A&AS, 45, 85

– 11 –

Giuricin, G., Mardirossian, F., & Mezzetti, M. 1983, ApJS, 52,35

Graff, K. 1922, AN, 217, 349

Grauer, A. D., McCall, J., Reaves, L. C., & Tribble, T. L. 1977, AJ, 82, 740

Gulmen, O, Sezer, C. & Gudur, N. 1985, A&AS, 60, 389

Hall,D. S. 1976, in IAU Colloq. No. 29, Multiple Periodic Variable Stars, ed. W. S. Fitch (Dor-

drecht:Reidel), 287

Hall, D. S. 1989, Space Sci. Rev., 50, 219

Hall, D. S. 1991, ApJ, 380, L85

Hall, D. S., Cannon III, R. O., & Rhombs, C. G. 1973, PASP, 85, 420

Hall, D. S. & Kreiner, J.M. 1980, Acta Astron., 30, 287

Hall, D. S. & Stuhlinger, T., 1976, Acta Astron., 26, 109

Hall, D. S. and Wawrukiewicz, A. S. 1972, PASP, 84, 541

Hall, D. S. & Woolley, K. S., 1973, PASP, 85, 618

Hayasaka, T. 1979 PASJ, 31, 271

Helt, B. E. 1987, A&A, 172, 155

Hobart, M. A., Pena, J. H., Peniche, R., Rodriguez, E., Garrido, R., Rios-Berumen, M., Rios-

Herrera, M., & Lopez-Cruz, O. 1994 Revista Mexicana de Astronomia y Astrofisica, 28,

111

Koch, R. H. 1960, AJ, 65, 139

Koch, R. H. 1962, AJ, 67, 130

Koch, R. H. 1963, AJ, 68, 785

Kopal, Z. 1978, Dynamics of close binary systems (Dordrecht:D. Reidel)

Kreiner, J. M. 1971, Acta. Astron., 21, 365

Kreiner, J. M. & Tremko, J. 1988, BAICz, 39, 73

Kreiner, J. M. & Ziolkowski, J. 1978, Acta Astron., 28, 497

Kulkarni, A. G. & Abyankar, K. D. 1980, Ap&SS, 67, 205

Kwee, K. K., and van Woerden, H. 1956, Bull. Astron. Inst. Netherlands, 12, 357

– 12 –

Kwee, K. K., and van Woerden, H. 1958, Bull. Astron. Inst. Netherlands, 485, 131

Lanza, A. F. & Rodono, M. 1999, A&A, 349, 887

Lanza A.F., Rodono M., Rosner, R. 1998, MNRAS, 296,893

Lu, W. 1992, Acta Astronomica, 42, 73

Mallama, A. D. 1982, Communications of the IAPPP, 7, 14

Marsh, T.R. & Pringle, J.E. 1990, ApJ, 365, 677

Massey, P. & Jacoby, G. H. 1992 in ASP Conf. Ser. 23, Astronomical CCD Observing and Reduction

Techniques, ed. S. B. Howell (San Francisco:ASP), 240

Mayer, P. 1984, BAICz, 35, 180

McCook, G. P. 1971, AJ, 76, 449

Narusawa, S., Nakamura, Y. & Yamasaki, A. 1994, AJ, 107. 1141

Olson, E. C. 1989 AJ, 98, 1002

Parthasarathy, M. & Sarma, M. B. K. 1980, Ap&SS, 72, 477

Parker, E.N. 1979, Cosmical magnetic fields (Oxford:Clarendon Press)

Plavec, M. J., & Dobias, J. J. 1987, AJ, 93, 171

Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Numerical Recipes in

Fortran 77 (2nd ed.; Cambridge: Cambridge University Press)

Quester, W. 1968, IBVS, 283

Qian, S. 2000a, AJ, 119, 901

Qian, S. 2000b, A&AS, 146, 377

Qian, S. 2001, AJ, 121, 1614

Qian, S., Liu, Q., & Yang, Y. 1998, Publications of the Yunnan Observatory, 75, 1

Richards, M. T. 1990, ApJ, 350, 372

Richards, M. T. & Albright, G. E. 1993, ApJS, 88 199

Rovithis-Livaniou, H., Kranidiotis, A. N., Rovithis, P., & Athanassiades, G. 2000, A&A, 354, 904

Rovithis-Livaniou, H. & Rovithis, P., 2001 in ASP Conf. Ser. 229, Evolution of Binary and Multiple

Star Systems, ed. Ph. Podsiadlowski, S, Rappaport, A. R. King, F. D’Antona & L. Burderi

(San Francisco:ASP) 2001

– 13 –

Schoeffel, E. 1977, A&A, 61, 107

Schultz, E. & Walter, K. 1977, A&AS, 29, 51

Shenghong, G., Quingyao, L., Yulan, Y., Bi, W., & Zhankui, H. 1994, IBVS, 4060, 1

Simon, V. 1996, A&A, 311, 915

Simon, V. 1997, A&A, 327, 1087

Sistero, R. F. 1971, BAICz, 22, 188

Sistero, R. F. Fourcade, C. R. & Laborde, J. R. 1969, IBVS, 402

Soderhjelm, S. 1980, A&A, 89, 100

Struve, O. 1946, ApJ, 104, 253

Taylor, M. 1981, JAAVSO, 10, 83

Tout, C. A. & Hall, D. S. 1991, MNRAS, 253, 9

Yoon, T. S., Honeycutt, R. K., Kaitchuck, R. H., and Schlegel, E. M. 1994, PASP, 106, 239

Walter, K. 1976, A&AS, 26, 227

Warner, B. W. 1988, Nature, 336, 129

This preprint was prepared with the AAS LATEX macros v5.0.

– 14 –

150 160 170 180 190

16

14

12

10

8

Oct1198

Sep0198

Aug2298

Fig. 1.— V light curves for the eclipses observed in 1998 on the indicated UT dates. August and

October data are offset by −2 and +2 magnitudes respectively. Comparison star differences are

shown at the bottom.

– 15 –

0 2000 4000 6000 8000 10000

0

0.2

0.4

0.6

1900 1920 1940 1960 1980 2000

Fig. 2.— O−C plot for WW Cyg with respect to Graff’s ephemeris (equation 2). The top label

shows approximate calendar years of the observations. The solid line represents the best fit parabola

to the data (equation 3). Data for epochs < 7500 are from Hall & Wawrukiewicz (1972).

– 16 –

0 5000 10000-0.1

-0.05

0

0.05

Fig. 3.— The O−C residuals in days for WW Cyg after subtraction of the best-fit parabola given

by equation 3.

– 17 –

0.0002 0.0004 0.0006 0.0008 0.0010

0.005

0.01

0.015

0.02

Fig. 4.— Fourier transform of the data shown in Figure 3 (solid line). The dashed line is the

Fourier transform after subtraction of the waveform in equation 6.

– 18 –

-0.1

-0.05

0

0.051900 1920 1940 1960 1980 2000

0 5000 10000

-0.05

0

Fig. 5.— Figure 5a shows the residuals of fig. 3 with equation 6 plotted as the solid line. Figure 5b

shows the residuals after the curve shown in Figure 5a is subtracted from the data. Approximate

calendar years appear along the top.

– 19 –

Fig. 6.— Plot of mass ratio Q versus secondary spectral type taken from Hall (1989). A horizontal

line indicates no period change noted, / indicates a period increase only, \ indicates a period

decrease only, and an X indicates both increases and decreases of the period. A • is used for

systems for which no conclusion about the period trend could be drawn.

– 20 –

0

10

20

30

40

F4 G0 K0 M0

Fig. 7.— Plot of binary period P in days versus secondary spectral type for the Algols listed in

Table 3. The type of period change follows the convention adopted in Figure 6.

– 21 –

Table 1. Observed Primary Minima of WW Cygni.

Epoch of Minimum Band Number of Points

(HJD −2450000)

387.6074 ± 0.0005a R —

1047.8520 ± 0.0006 V 53

1057.8047 ± 0.0002 V 206

1097.6198 ± 0.0002 V 120

aBuckner et al. (1998)

– 22 –

Table 2. O−C data for WW Cygnia.

HJD Epoch O−C Ref.

(−2400000)

42965.739 7315 0.346 1

43320.734 7939 0.391 1

43413.638 7967 0.400 1

43665.786 8043 0.405 1

44083.831 8169 0.422 1

44531.721 8304 0.426 1

44813.738 8389 0.441 1

44856.874 8402 0.447 1

44896.689 8414 0.450 1

45168.747 8496 0.458 1

45221.829 8512 0.457 1

45261.643 8524 0.459 1

45523.750 8603 0.470 1

45523.751 8603 0.471 1

45888.708 8713 0.484 1

46253.661 8823 0.492 1

46286.839 8833 0.493 1

46568.845 8918 0.497 1

46774.552 8980 0.508 1

47006.790 9050 0.509 1

47109.640 9081 0.511 1

47716.793 9264 0.529 1

47799.737 9289 0.531 1

47809.683 9292 0.524 1

48801.711 9591 0.567 1

50387.6074 10069 0.6144 2

51047.8520 10268 0.6414 3

51057.8047 10271 0.6411 3

51097.6198 10283 0.6441 3

aBased on ephemeris of Graff (1922)

References. — (1) Baldwin &

Samolyk (1995); (2) Buckner et al.

(1998); (3) This work

– 23 –

Table 3. Period changes of Algols with convective secondaries.

Star Sec. P Type of Ref. Star Sec. P Type of Ref.

Sp.T. (days) ∆P Sp.T. (days) ∆P

TW And K2a 4.1228 / 1 AD Her K4 9.7666 − 29

XZ And G9 1.3573 X 2 SZ Her G8-G9 0.8181 X 1,27

RY Aqr K1 1.9666 / 3 UX Her K6 1.5489 X 1,28

KO Aql K6-K7 2.8640 / 4 V338 Her K6 1.3057 • 1

V346 Aql G8-G9 1.1064 • 5 RX Hya M5 2.2816 X 30

RW Ara K2-K3 4.3674 • 6 TT Hya K0 6.9534 • 31

IM Aur F9 1.2473 • 7 Y Leo K5 1.6861 X 1

SU Boo K2 1.5612 − 1 RS Lep M0 1.2885 − 32

S Cnc K2 9.4846 − 8 δ Lib K2 2.3274 / 28,33

RZ Cnc K4III 21.6430 − 9 RV Oph K0 3.6871 − 1

RZ Cas K3-K4 1.1953 X 11 UU Oph G8-G9 4.3968 • 34

TV Cas K3 1.8126 X 12 DN Ori F5IIIc 12.9663 • 35

TW Cas K4-K5 1.4283 \ 13 AQ Peg K3-K4 5.5485 X 1

CV Car K4 14.4149 • 10 AT Peg K6 1.1461 X 36

U Cep G3-G4 2.4930 X 1 AW Peg G3-G4 10.6225 − 50

RS Cep G8III-IVb 12.4199 / 15 DI Peg K0 0.7118 X 37

XY Cep K4-K5 2.7745 \ 16 β Per K4 2.8673 X 43

U CrB K2-K3 3.4522 X 1 RT Per K2-K3 0.8494 X 1

RW CrB K6-K7 0.7264 \ 17 RW Per K2-K3 13.1939 X 38

UZ Cyg K4 31.3058 − 18 RY Per F5g 6.8636 − 1

WW Cyg G9 3.3178 X 19,20 Y Psc K4 3.7658 X 1

ZZ Cyg K6 0.6286 − 1 U Sge K0 3.3806 X 39

KU Cyg K5III 39.4393 • 8 V505 Sgr K5 1.1829 X 40

V548 Cyg K3-K4 1.8053 • 21 HU Tau K3-K4 2.0563 − 41

W Del K1-K2 4.8060 X 1 RW Tau M0 2.7688 X 42

Z Dra K3-K4 1.3574 X 1 X Tri K0 0.9715 X 44

TW Dra K0 2.8069 X 1 TX UMa K5 3.0632 X 1

AI Dra K3 1.1988 X 22 VV UMa G6 0.6874 X 45

S Equ K0-K1 3.4361 X 1 S Vel K3-K4 5.9336 • 46

AS Eri K0 2.6642 • 24 DL Vir K1-K2 1.3155 / 47

AL Gem K4 1.3913 − 25 RS Vul F7 4.4777 − 8

RY Gem K2 9.3009 \ 23 BE Vul K2-K3 1.5520 \ 48

X Gru K4-K5 2.1236 / 26 V78 ωCen K2-K3 1.1681 • 49

aRef. 19

bRef. 14

cRef. 35

References. — (1) Kreiner 1971; (2) Demircan et al. 1995; (3) Helt 1987; (4) Hayasaka 1979; (5) Quester

1968; (6) Walter 1976; (7) Gulmen et al. 1985; (8) Kreiner & Ziolkowski 1978; (9) Olson 1989; (10) Giuricin &

Mardirossian 1981; (11) Narusawa, Nakamura, & Yamasaki 1994; (12) Grauer 1977; (13) McCook 1971; (14)

Plavec & Dobias 1987; (15) Hall, Cannon & Rhombs 1973; (16) Kreiner & Tremko 1988; (17) Qian 2000a; (18)

Hall & Woolley 1973; (19) Yoon et al. 1994; (20) This work (21) Ertan 1981; (22) Degirmenci et al. 2000;

(23) Hall & Stuhlinger 1976; (24) Koch 1960; (25) Koch 1963; (26) Schultz & Walter 1977; (27) Baldwin &

Samolyk 1997; (28) Baldwin & Samolyk 1996; (29) Batten & Fletcher 1978; (30) Qian 2000b; (31) Kulkarni

& Abyankar 1980; (32) Shenghong et al. 1994; (33) Koch 1962; (34) Taylor 1981; (35) Etzel & Olson 1995;

(36) Rovithis-Livaniou & Rovithis 2001; (37) Lu 1992; (38) Mayer 1984; (39) Simon 1997; (40) Qian, Liu, &

Yang 1998; (41) Parthasarathy & Sarma 1980; (42)Frieboes-Conde & Herczeg 1973; (43) Soderhjelm 1980; (44)

Rovithis-Livaniou et al. 2000; (45) Simon 1996; (46) Sistero 1971; (47) Schoeffel 1977; (48) Qian 2001; (49)

Sistero, Fourcade & Laborde 1969; (50) Derman & Demircan 1992.